Average Error: 3.1 → 0.1
Time: 27.5s
Precision: 64
Internal Precision: 576
$1 - \frac{1}{a} \cdot {\left(1 - b\right)}^{\left(\frac{3}{2}\right)}$
$1 - \frac{{\left(1 - b\right)}^{\left(\frac{1}{2} \cdot \frac{3}{2}\right)}}{\frac{a}{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}}$

# Try it out

Results

 In Out
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# Derivation

1. Initial program 3.1

$1 - \frac{1}{a} \cdot {\left(1 - b\right)}^{\left(\frac{3}{2}\right)}$
2. Applied simplify3.1

$\leadsto \color{blue}{1 - \frac{{\left(1 - b\right)}^{\left(\frac{3}{2}\right)}}{a}}$
3. Using strategy rm

$\leadsto 1 - \frac{{\color{blue}{\left(\sqrt{1 - b} \cdot \sqrt{1 - b}\right)}}^{\left(\frac{3}{2}\right)}}{a}$
5. Applied unpow-prod-down3.2

$\leadsto 1 - \frac{\color{blue}{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}}{a}$
6. Applied associate-/l*0.2

$\leadsto 1 - \color{blue}{\frac{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}{\frac{a}{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}}}$
7. Using strategy rm
8. Applied pow1/20.2

$\leadsto 1 - \frac{{\color{blue}{\left({\left(1 - b\right)}^{\frac{1}{2}}\right)}}^{\left(\frac{3}{2}\right)}}{\frac{a}{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}}$
9. Applied pow-pow0.1

$\leadsto 1 - \frac{\color{blue}{{\left(1 - b\right)}^{\left(\frac{1}{2} \cdot \frac{3}{2}\right)}}}{\frac{a}{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}}$

# Runtime

Time bar (total: 27.5s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (a b)
:name "(1 - 1/a*(1 - b)^(3/2))"
(- 1 (* (/ 1 a) (pow (- 1 b) (/ 3 2)))))